%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU134+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 15:22:31 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   64 (  24 unt;   0 def)
%            Number of atoms       :  121 (  40 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  108 (  51   ~;  40   |;   7   &)
%                                         (   5 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   44 (  34   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f78,plain,
    $false,
    inference(avatar_sat_refutation,[],[f53,f65,f67,f70,f72,f75,f77]) ).

fof(f77,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f76]) ).

fof(f76,plain,
    ( $false
    | spl4_2 ),
    inference(global_subsumption,[],[f31,f32,f40,f41,f36,f33,f34,f35,f43,f30,f39,f37,f59,f58,f38,f60,f61,f73,f51]) ).

fof(f51,plain,
    ( ~ subset(sK0,sK1)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f50,plain,
    ( spl4_2
  <=> subset(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f73,plain,
    empty_set != set_difference(sK0,sK1),
    inference(subsumption_resolution,[],[f31,f37]) ).

fof(f61,plain,
    ! [X0] :
      ( empty_set = set_difference(X0,empty_set)
      | empty_set != X0 ),
    inference(resolution,[],[f38,f58]) ).

fof(f60,plain,
    ! [X0] : empty_set = set_difference(X0,X0),
    inference(resolution,[],[f38,f36]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | empty_set = set_difference(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).

fof(f58,plain,
    ! [X0] :
      ( subset(X0,empty_set)
      | empty_set != X0 ),
    inference(superposition,[],[f37,f34]) ).

fof(f59,plain,
    ! [X0] : subset(empty_set,X0),
    inference(trivial_inequality_removal,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( empty_set != empty_set
      | subset(empty_set,X0) ),
    inference(superposition,[],[f37,f33]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

fof(f30,plain,
    ( subset(sK0,sK1)
    | empty_set = set_difference(sK0,sK1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ( ( ~ subset(sK0,sK1)
      | empty_set != set_difference(sK0,sK1) )
    & ( subset(sK0,sK1)
      | empty_set = set_difference(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23]) ).

fof(f23,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(X0,X1)
          | empty_set != set_difference(X0,X1) )
        & ( subset(X0,X1)
          | empty_set = set_difference(X0,X1) ) )
   => ( ( ~ subset(sK0,sK1)
        | empty_set != set_difference(sK0,sK1) )
      & ( subset(sK0,sK1)
        | empty_set = set_difference(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ? [X0,X1] :
      ( ( ~ subset(X0,X1)
        | empty_set != set_difference(X0,X1) )
      & ( subset(X0,X1)
        | empty_set = set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <~> subset(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1] :
        ( empty_set = set_difference(X0,X1)
      <=> subset(X0,X1) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(f43,plain,
    empty_set = sK3,
    inference(resolution,[],[f35,f41]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f34,plain,
    ! [X0] : set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : set_difference(X0,empty_set) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

fof(f33,plain,
    ! [X0] : empty_set = set_difference(empty_set,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : empty_set = set_difference(empty_set,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

fof(f36,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f41,plain,
    empty(sK3),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    empty(sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f2,f28]) ).

fof(f28,plain,
    ( ? [X0] : empty(X0)
   => empty(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f40,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ~ empty(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f3,f26]) ).

fof(f26,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f3,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f32,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f31,plain,
    ( ~ subset(sK0,sK1)
    | empty_set != set_difference(sK0,sK1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f75,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f74]) ).

fof(f74,plain,
    ( $false
    | ~ spl4_1 ),
    inference(global_subsumption,[],[f31,f32,f40,f41,f36,f33,f34,f35,f43,f30,f39,f37,f59,f58,f38,f60,f61,f48,f73]) ).

fof(f48,plain,
    ( empty_set = set_difference(sK0,sK1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f46,plain,
    ( spl4_1
  <=> empty_set = set_difference(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f72,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f71]) ).

fof(f71,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f48,f31,f32,f40,f41,f36,f33,f34,f35,f43,f30,f52,f39,f37,f59,f58,f38,f60,f61,f62,f68]) ).

fof(f68,plain,
    ( empty_set != set_difference(sK0,sK1)
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f31,f52]) ).

fof(f62,plain,
    ( empty_set = set_difference(sK0,sK1)
    | ~ spl4_2 ),
    inference(resolution,[],[f38,f52]) ).

fof(f52,plain,
    ( subset(sK0,sK1)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f70,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f69]) ).

fof(f69,plain,
    ( $false
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f31,f32,f40,f41,f36,f33,f34,f35,f43,f30,f52,f39,f37,f59,f58,f38,f60,f61,f62,f68]) ).

fof(f67,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f66]) ).

fof(f66,plain,
    ( $false
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f31,f32,f40,f41,f36,f33,f34,f35,f43,f30,f52,f39,f37,f59,f58,f38,f60,f61,f62]) ).

fof(f65,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f64]) ).

fof(f64,plain,
    ( $false
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f62,f47]) ).

fof(f47,plain,
    ( empty_set != set_difference(sK0,sK1)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f53,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f30,f50,f46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU134+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 21:08:48 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (22138)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (22142)WARNING: value z3 for option sas not known
% 0.14/0.37  % (22142)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (22142)First to succeed.
% 0.14/0.37  % (22142)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (22142)------------------------------
% 0.14/0.37  % (22142)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.37  % (22142)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (22142)Memory used [KB]: 774
% 0.14/0.37  % (22142)Time elapsed: 0.004 s
% 0.14/0.37  % (22142)Instructions burned: 5 (million)
% 0.14/0.37  % (22142)------------------------------
% 0.14/0.37  % (22142)------------------------------
% 0.14/0.37  % (22138)Success in time 0.013 s
%------------------------------------------------------------------------------